# How do you solve x + y = 4 and y = 2x + 1?

Mar 24, 2018

Using substitution, you can find the solution is $x = 1 , y = 3$

#### Explanation:

The second expression $y = 2 x + 1$ is already an expression ready to substitute! Since we know what $y$ is equivalent to, we can substitute it into the first expression:

$x + y = 4$

$x + \left(2 x + 1\right) = 4 \Rightarrow x + 2 x + 1 = 4$

$x \left(1 + 2\right) + 1 = 4 \Rightarrow 3 x + 1 = 4$

$3 x \cancel{+ 1 - 1} = 4 - 1 \Rightarrow 3 x = 3$

$\textcolor{red}{x = 1}$

Now that we know what $x$ is equivalent to, we can solve for $y$

$y = 2 x + 1 \Rightarrow y = 2 \left(1\right) + 1 = 2 + 1$

$\textcolor{b l u e}{y = 3}$